Question

Fourth root of 0.0016 is a surd or not ?

Answer 1

Answer: Fourth root of 0.0016 is not a surd number (it is rational number).

If we know
`2^(4) = 16`, exponentiate number 10 times less:


`image`

And now we can use:

`0.0016 = 0.2^(4)`

Now we take root from it:

`\sqrt[4]{0.2^(4)}`

We can use formula:

`\sqrt[m]{a^(m)} = a`

Replace values from formula:


`image`

And 0.2 is a rational number, so that number is not surd.

Hope this helps!